Solution A contains equal amount of alcohol and water in it.

AAPL wrote:e-GMAT

Solution A contains equal amount of alcohol and water in it. It is heated till 50 percent of the water in solution A evaporates. Solution B, whose volume is equal to the reduced volume of water in Solution A, is then added to Solution A and the volume of alcohol in the resultant solution is equal to 12 liters. If solution B contains alcohol and water in the ratio 2:3, how many more liters of water should be added to the resultant solution to increase the concentration of water in the resultant solution to 50 percent?

A. 2
B. 4
C. 6
D. 8
E. 12

OA B

Say the ratio of alcohol and water in Solution A is 1 : 1; thus, after heating, the revised ratio = 1 : 1/2 => 2 : 1. Say the actual quantity of alcohol is 2x, thus, the actual quantity of water is x and the quantity of Solution A = 3x.

=> Total quantity of Solution B = x

Given that if solution B contains alcohol and water in the ratio 2 : 3, the quantity of alcohol = 2x/5 and the quantity of water = 3x/5.

=> 2x + 2x/5 = 12 => x = 5

• Solution A: quantity of alcohol = 2x = 10 and quantity of water = 5
• Solution B: quantity of alcohol = 2x/5 = 2 and quantity of water = 3x/5 = 3

After the mixing up, we get of Solution A and B, we get the quantity of alcohol = 10 + 2 = 12 and quantity of water = 5 + 3 = 8.

Say y liters of water is added so that the resultant solution increases the concentration of water in the resultant solution to 50 percent.

Thus, alcohol : water :: 50% : 50% => 12 : (8 + y) :: 50% : 50% => 12 = (8 + y) => y = 4 ltres

The correct answer: B

Hope this helps!

-Jay
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